A347060 Total number of 1's in the binary expansion of parts in all partitions of n into distinct parts.

0, 1, 1, 4, 4, 7, 11, 15, 20, 28, 39, 48, 64, 80, 104, 134, 167, 203, 257, 311, 381, 470, 566, 680, 820, 981, 1168, 1394, 1650, 1946, 2300, 2700, 3161, 3705, 4315, 5026, 5845, 6769, 7827, 9049, 10424, 11992, 13784, 15801, 18088, 20702, 23620, 26922, 30665

Offset: 0

Author

Alois P. Heinz, Aug 14 2021

Keywords

• nonn
• base

Examples

			a(5) = 7 counts the 1's in [101], [100, 1], [11, 10].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A000120, A066189, A066624, A318756, A319140.

Programs

Maple

h:= proc(n) option remember; add(i, i=Bits[Split](n)) end:
b:= proc(n, i) option remember; `if`(n=0, [1, 0],
      `if`(n>i*(i+1)/2, 0, b(n, i-1)+(p-> p+
       [0, p[1]*h(i)])(b(n-i, min(n-i, i-1)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..60);